Rotating flows can become unstable through the so-called triadic resonance [1]}, i.e. a base flow with frequency \(\omega _0\)  and azimuthal wavenumber \(m_0\)  can excite two inertial waves whose frequencies \(\omega _1,\, \omega _2\)  and azimuthal wavenumbers \(m_1,\,m_2\)  match the resonance conditions  [2]}, [3]} Here we present the resonance conditions in a spherical geometry. In an unbounded domain, the second condition should read \({k}_1\pm {k}_2={k}_0\) , where \(k\)  is the wave vector.
\(\omega _2\pm \omega _1=\omega _0, \quad m_2\pm m_1=m_0.\) 
